Given the function f(x, y) = V10 – x + y, evaluate f(2, 1) and f(-9, –3).

Q: How many independent variables does the function r(t) = ⟨ƒ(t), g(t), h(t)⟩ have?

A: Given that the functions f, g, and h, all depend on t. t is independent So there is only one…

Q: Find the largest domain (in R²) for the function 1+ Vx + /y x2 + y2 f (x, y) :

A: Given that, fx,y=1+x+yx2+y2 To determine, the largest domain in ℝ2 for fx,y

Q: For the function f(x)=4x2-4xy+2y2, start at (xo,yo)= (2,4) and proceed according to the vertical…

A: This question is about application of differential equation

Q: Find of the function x³ z2 – 5æyz = a? + y %3D

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Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: If f(x,y)=xe/2+118x?y, then asf at (1,1) is equal to əx²əy³

A: Given function is: f(x,y)=xey22+118x2y3 Derivative of function with respect to 'x'…

Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

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Q: find the domain of the given function. Vx²-2y ,2. f ( x, y ) : .A D= {(x,y) ER?: y s 2x²} .B D= {…

A: Option (B) is correct

Q: The Range of y = [2x + 1] is Z, T O F

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Q: Given f(x, y) = 12/8x* + 6y + 2xy°, find f. (x, y) = f,(x, y) =

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Q: Given the function f(x) = x(x – 3)(x + 2), find 1) its y-intercept: 2) its x-intercepts: 3) As x →…

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Q: find the specific function values. ƒ(x, y) = x2 + xy5 ƒ(2, 3)

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Q: For the function f(x,y) = 5y + x, find f(3, – 5), f(- 1,4), f(- 3, – 4), and f(0,7).

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Q: Find a linear approximation of the function f(x) = V1+x at a = 0, and use it to approximate the…

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Q: Find fry for the function f(x, y) = x²? – xy? – 7y +3. %3D

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Q: Suppose that f(x, y) = e² / y on the domain D = {(x, y) | 0 < y < 2,0 < x < y³}. D

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Q: Examine the function f(x, y) =-3x-4y+15x - 16y + 6 for relative extrema.

A: Here we have to find relative maximum.  The solution is in both 1st and second steps.

Q: The range of the function f(x, y) = 1 3+Vx+y is equal to:

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Q: Find domain and range F(x,y)= Vx-1

A: Since you have asked multiple questions in a single request, as per policy, only the first question…

Q: Find y as a function of a if r'y" - 5ay + 9y = r, y(1) = 9, y'(1) = 3.

A: Given: x2y ''-5xy'+9y=x9, y(1)=9, y'(1)=3 Consider Homogenous differential equation  x2y''-5xy'+9y=0…

Q: Given the functions f (2) = 3z? – x,g (x) =.h (z) = 9z, find hog (1) O - 252 %3D %3D %3D O 234 O -36…

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Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: find the domain of the given function. f ( x , y ) = Vx²-2y .A D = {(x.y) ER?: y 2x²} .B D= {(x, y)…

A: We find domain of given function

Q: For the function f(x,y) = 3x2 + 7y2, find the following. f(x +h,y) – f(x,y) а.

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Q: For the function y = f(x) = x² – 2x, x x ≥ 1, find (ƒ-¹) '(3) = df-1 dy y=3

A: We have to find the f-1'(3).

Q: Find all points (x, y) where the functions f(x), g(x), h(x) have the same value: f(x) = 2x−5 + 3 ,…

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Q: f) Given w=(x+y)/(z-3y) , Find dw

A: Total derivative

Q: Given the function: f(x, y) = 3x°y² – 72²y+ 5x – 4y Find the folowing: show complete solution fzy(x,…

A: Given:      fx,y=3x3y2-7x2y+5x-4y   a) fxyx,y:     fxyx,y=∂2∂y∂x=∂∂y∂∂x…

Q: For the function y df-1 f(x) = a? – x + 2, x > 0.5, find dy y=10 (f-1)'(10).

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Q: Find dz implicitly of the relation r + y³ = 3ry.

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Q: Find fyx, y) for the function flx,y)=x*-7x3y2+6xy³ + 4y4 O-28y O -15y2 O 76x2 O 24x

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Q: Find the indicated value of the function f(x,y,z) = 6x – 7y + 2z° - 3. f(3, – 4,2) f(3, – 4,2) =

A: The given function is, The values of x, y and z are,

Q: Q1: Find and : for the function ax af ду f(x, y) = x+y %3D y2+x3

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Q: Given f (z, y) - 3z +2y +1, find the value. %3D 5 (§. ±) - The value of f

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Q: For the function f(x,y) = e9xy, find fx and fy. fx = ? fy = ?

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Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

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Q: For the function f(x,y) = e 12xy, find f, and f,.

A: The given function is  f(x, y) = e12xy To find fx, fy

Q: Q17 It z = f(x, y) and z* - x² = x²y°z? * and dz Find:

A: We will use basic differential calculus to solve the three parts of this question.

Q: ôf What is for the same function f = x*y+3y'z² ? ду X,Z

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Q: For the given functions, find the domain of the function. a) f(x,y,z) = - 36-4x²–9y² –z² b) f(x,y,z)…

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Q: Consider the function f(x, y) = x² + xy - 5x- y+1. Then:

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Q: find the specific function values ƒ(x, y) = x2 + xy3 a. ƒ(0, 0) b. ƒ(2, 3)

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Q: Find the linear approximation of the function f(x) = V1-x at a = 0 and use it to approximate the…

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Q: For the function: f(z) = – 5z² + 6, %3D f(z) – f(a) Preview

A: Given f(x) = -5x2+6 then f(a) = -5a2+6

Q: Q2) Find Fx, Fyy and Fyx For the function F(x.y) = (x+y) + (y +1)* .

A: Note :- Due to our guidelines, we can solve only one question, plz upload rest question again by…

Q: For f(x,y) = Inx+y³, find f( e 5,6). f( e 5,6) = [

A: We have to find f( e5 , 6)

Q: Evaluate F-dr where C is represented by r(t). C F(x, y)=xyi+yj C: r(t)=28ti+tj, 0≤t≤7

A: To find ∫CF·dr

Q: For the function f(x,y)= x + 4y 3 4 x +y find f, fy, f(5,-5), and f,(1,3).

A: For the function fx, y=x2+4y3x3+y4, to find fx, fy, fx5, -5, and fy1, 3.

Q: find the domain of the given function. f (| x , у) %3D Vx²-2y .A D= { (x, y) ER?: ys x } 2 .B D =…

A: